diff --git a/sphinx/application.py b/sphinx/application.py
index 44432f8a6..b42fb9dba 100644
--- a/sphinx/application.py
+++ b/sphinx/application.py
@@ -1030,9 +1030,6 @@ class Sphinx:
             kwargs['defer'] = 'defer'
 
         self.registry.add_js_file(filename, priority=priority, **kwargs)
-        if hasattr(self, 'builder') and hasattr(self.builder, 'add_js_file'):
-            self.builder.add_js_file(filename,
-                                     priority=priority, **kwargs)
 
     def add_css_file(self, filename: str, priority: int = 500, **kwargs: Any) -> None:
         """Register a stylesheet to include in the HTML output.
@@ -1093,9 +1090,6 @@ class Sphinx:
         """
         logger.debug('[app] adding stylesheet: %r', filename)
         self.registry.add_css_files(filename, priority=priority, **kwargs)
-        if hasattr(self, 'builder') and hasattr(self.builder, 'add_css_file'):
-            self.builder.add_css_file(filename,
-                                      priority=priority, **kwargs)
 
     def add_latex_package(self, packagename: str, options: str | None = None,
                           after_hyperref: bool = False) -> None:
diff --git a/sphinx/builders/html/__init__.py b/sphinx/builders/html/__init__.py
index 10e8ce0e2..1d0953cb8 100644
--- a/sphinx/builders/html/__init__.py
+++ b/sphinx/builders/html/__init__.py
@@ -498,9 +498,15 @@ class StandaloneHTMLBuilder(Builder):
                 rellinks.append((indexname, indexcls.localname,
                                  '', indexcls.shortname))
 
+        # add assets registered after ``Builder.init()``.
+        for css_filename, attrs in self.app.registry.css_files:
+            self.add_css_file(css_filename, **attrs)
+        for js_filename, attrs in self.app.registry.js_files:
+            self.add_js_file(js_filename or '', **attrs)
+
         # back up _css_files and _js_files to allow adding CSS/JS files to a specific page.
-        self._orig_css_files = list(self._css_files)
-        self._orig_js_files = list(self._js_files)
+        self._orig_css_files = list(dict.fromkeys(self._css_files))
+        self._orig_js_files = list(dict.fromkeys(self._js_files))
         styles = list(self._get_style_filenames())
 
         self.globalcontext = {
diff --git a/sphinx/ext/mathjax.py b/sphinx/ext/mathjax.py
index d620002d5..0131a9441 100644
--- a/sphinx/ext/mathjax.py
+++ b/sphinx/ext/mathjax.py
@@ -14,6 +14,7 @@ from docutils import nodes
 
 import sphinx
 from sphinx.application import Sphinx
+from sphinx.builders.html import StandaloneHTMLBuilder
 from sphinx.domains.math import MathDomain
 from sphinx.errors import ExtensionError
 from sphinx.locale import _
@@ -79,6 +80,7 @@ def install_mathjax(app: Sphinx, pagename: str, templatename: str, context: dict
                              'mathjax extension to work')
 
     domain = cast(MathDomain, app.env.get_domain('math'))
+    builder = cast(StandaloneHTMLBuilder, app.builder)
     if app.registry.html_assets_policy == 'always' or domain.has_equations(pagename):
         # Enable mathjax only if equations exists
         if app.config.mathjax2_config:
@@ -87,10 +89,10 @@ def install_mathjax(app: Sphinx, pagename: str, templatename: str, context: dict
                     'mathjax_config/mathjax2_config does not work '
                     'for the current MathJax version, use mathjax3_config instead')
             body = 'MathJax.Hub.Config(%s)' % json.dumps(app.config.mathjax2_config)
-            app.add_js_file(None, type='text/x-mathjax-config', body=body)
+            builder.add_js_file('', type='text/x-mathjax-config', body=body)
         if app.config.mathjax3_config:
             body = 'window.MathJax = %s' % json.dumps(app.config.mathjax3_config)
-            app.add_js_file(None, body=body)
+            builder.add_js_file('', body=body)
 
         options = {}
         if app.config.mathjax_options:
@@ -102,7 +104,7 @@ def install_mathjax(app: Sphinx, pagename: str, templatename: str, context: dict
             else:
                 # Load other MathJax via "async" method
                 options['async'] = 'async'
-        app.add_js_file(app.config.mathjax_path, **options)
+        builder.add_js_file(app.config.mathjax_path, **options)
 
 
 def setup(app: Sphinx) -> dict[str, Any]: